A certain alloy is composed of two metals, A and B. A student wants to know the relationship between the metal ratio and the wavelength of the alloy. He conducted an experiment measuring ``the wavelength $y$ (in nanometers) of an alloy with A comprising $x\%$'' and plotted 20 data points $(x_k, y_k)$, $k = 1, \cdots, 20$, on the $xy$ plane. The regression line (best-fit line) is $y = 21.3 x - 40$.
To comply with submission standards, the report must be described as ``the wavelength $v$ (in micrometers) of an alloy with B comprising $u\%$''. He converted the data $(x_k, y_k)$ to $(u_k, v_k)$, $k = 1, \cdots, 20$, and obtained the regression line on the $uv$ plane as $v = a u + b$. Given that 1 nanometer $= 10 ^ { - 9 }$ meter and 1 micrometer $= 10 ^ { - 6 }$ meter. Select the correct options.
(1) $u _ { k } = 100 - x _ { k } , k = 1 , \cdots , 20$
(2) $v _ { k } = 1000 y _ { k } , k = 1 , \cdots , 20$
(3) The standard deviation of $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots , u _ { 20 }$ equals the standard deviation of $x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots , x _ { 20 }$
(4) $b = 2.09$
(5) The student found another data point $(u _ { 21 } , v _ { 21 })$ satisfying $v _ { 21 } = a u _ { 21 } + b$; if these 21 data points $(u_k, v_k)$, $k = 1, \cdots, 21$, are plotted on the $uv$ plane, the regression line is still $v = a u + b$